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PLAN 1.Briefly describe procedure for calculating the biases between the reconstructed and modeled brightness temperatures; 2.Summarize the latitudinally averaged bias trends observed in SMOS brightness temperatures over the last two years. 3.Examine the possile impact of geopysical parameters on the descending-ascending bias differences; 4.Examine the correlation between the alias-free field of view bias, the antenna patch physical temperature and the most important geophysical parameters; 5.Examine the time-latitude structure of the biases.

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HOW BIASES ARE COMPUTED We do not include gridpoints within director cosine units of the domain boundaries. Averages are computed over both the alias-free (AF) and extended alias-free (EAF) portions of the field of view (FOV). We do not include gridpoints within director cosine units of the domain boundaries. bias STEP 1: For each scene of each half-orbit, compute the domain average of the difference (or bias) between reconstructed and modeled Stokes vector elements in the instrument polarization basis (Tx, Ty, Uxy, and Vxy).

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HOW BIASES ARE COMPUTED STEP 2: Filtering of scenes/snapshots. Scenes are then examined for possible contamination by direct sun aliases, land, ice, or radio frequency interference which could impact the statistics. Several filters are applied as outlined in the next few slides:

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HOW BIASES ARE COMPUTED FILTER 1: Any gridpoint within 0.1 director cosine units of any direct sun alias are also excluded from the averaging procedure.

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HOW BIASES ARE COMPUTED FILTER 2: Any scene for which the maximum value of |Tx| or |Ty| over the fundamental hexagon exceeds 500 K, or for which the maximum value of |Uxy| exceeds 230 K is excluded from the averaging. This filter is applied after correction by an OTT.

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HOW BIASES ARE COMPUTED FILTER 3: A land and ice filter is applied. Any scene for which the fraction of land in the earth portion of the entire fundamental hexagon exceeds 0.02 is removed. Likewise, any scene for which the ice fraction exceeds 0.05 is removed. Finally, gridpoints closer than 80 km from land are removed.

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STEP 3: After the scene filtering, the filtered per-scene averages for all half-orbits for a given pass direction (ascending or descending) are collected into a set of global daily regular latitude-longitude grids, each with a grid spacing of 0.25 o in latitude and 1 o in longitude. These grids containing the per-scene filtered AF and EAF average biases. The plots below show, for both the reprocessing data (left) and the calibrated L1 test data(right) the number of ascending pass scenes collected in each gridbox over the entire period considered here (over two years). Reprocessing Data (1-Slope model)Calibrated L1 Test Orbits HOW BIASES ARE COMPUTED

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STEP 4: Creation of time-latitude profiles of bias (Hovmoller plots). For each day, each pass direction and each latitude, the (filtered) AF and EAF biases (as well as domain averaged geophysical parameters and model brightness temperatures) are averaged over all longitudes: HOW BIASES ARE COMPUTED averaging over longitudes Filtered daily bias maps Time-latitude (Hovmoller) maps

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STEP 5: Creation of latitudinally averaged bias curves: The time-latitude filtered and gridded domain (AF and EAF) averaged biases, geophysical parameters, and model solutions are averaged over a latitude band ranging from 60 o S to 5 o N. This is done for ascending and descending passes separately. The yellow box on the time-latitude Hovmoller plot (lower-left) shows the latitude band used for averaging. HOW BIASES ARE COMPUTED averaging over latitude AF and EAF bias trend curves for asc/desc passes Time-latitude (Hovmoller) maps

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NOTE: We have far fewer orbits for the calibrated L1 test than for the 1-slope Reprocessing data. But the bias results with the two methods are, nevertheless, are similar. The yellow boxes highlight latitude band used to compute the bias trend curves (ranging from 60 o S to 5 o N). Reprocessing Data (1-Slope model): The complete set of half-orbits obtained from ESA reprocessing campaign Calibrated L1 Test Orbits: A small subset of half-orbits processed by ESA on GPOD HOW BIASES ARE COMPUTED

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TEMPORAL FILTERING OF BIAS TRENDS STEP 6: Temporal filtering. After obtaining the domain and latitudinally averaged biases between brightness temperatures obtained from MIRAS and the forward ocean model (MIRAS-model), a running 10-day smoother is applied to smooth out the small-scale ripples in the time series. The impact of this filter is shown below for both the calibrated L1 test orbits (left) and the complete set of orbits from the first reprocessing. The results also illustrate the impact of the reduced set of orbits used to test the calibrated L1 method.

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TEMPORAL FILTERING OF BIAS TRENDS Note that the unfiltered bias curve for reprocessing 1-slope data (red curve, right panel) is smoother than that for the calibrated L1 data (red curve, left panel) because these curves are averages over both longitude and latitude, and as we saw on the previous slides we have much more coverage in the reprocessing 1-slope data. Impact of smoothing much greater for Cal L1 than for the 1-Slope model owing to far fewer half-orbits in the average for Cal L1.

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A LOOK AT THE BIAS TRENDS Having established the method used to evaluate the bias between the reconstructed and model brightness temperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), we now move on to present the biases for both the most recent ESA reprocessing campaign, which employed the ‘1-slope’ loss model, and the ‘calibrated L1’ method recently proposed. Below is an outline of which follows: 1.Examination of biases averaged over longitude and latitude, including a look at coherence with variations in the corresponding average Tp7; 2.Examination of the potential impact of geophysical parameters on descending-ascending bias differences; 3.Examination of the correlation between bias variations and variations in Tp7 and several geophysical parameters; 4.Examination of time-latitude structure of the bias, which highlights the strong high-latitude bias variations late in each year.

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A LOOK AT THE BIAS TRENDS Having established the method used to evaluate the bias between the reconstructed and model brightness temperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), we now move on to present the biases for both the most recent ESA reprocessing campaign, which employed the ‘1-slope’ loss model, and the ‘calibrated L1’ method recently proposed. Below is an outline of which follows: 1.Examination of biases averaged over longitude and latitude, including a look at coherence with variations in the corresponding average Tp7; 2.Examination of the potential impact of geophysical parameters on descending-ascending bias differences; 3.Examination of the correlation between bias variations and variations in Tp7 and several geophysical parameters; 4.Examination of time-latitude structure of the bias, which highlights the strong high-latitude bias variations late in each year.

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IMPORTANT REMINDER BEFORE MOVING ON TO THE BIASES

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0.4 K/psu0.7 K/psu The sensitivity of L-band brightness temperature (Tx+Ty)/2=(Th+Tv)/2 to sea surface salinity depends upon the sea surface temperature (SST), but ranges from about -0.4 K/psu in cold water to about -0.7 K/psu in warm water. These are important numbers to keep in mind when we consider brightness temperature biases in what follows. (Tx+Ty)/2 bias +1 K SSS bias -2 psu (independent of incidence angle)

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BIAS TRENDS AVERAGED OVER LONGITUDE AND LATITUDE We begin by comparing AF and EAF descending and ascending pass bias trends for the calibrated L1 test (left) and the 1-slope reprocessing data (right).The trends are similar but there is an offset between the two methods. Most noticeable is the descending pass K dropoff around Sep-Nov, equivalent to a SSS increase of around 2 psu! Note that the dropoff is larger with Cal L1 than with the 1-slope model (yellow circles). This may be a result of differences in the set of half-orbits used for the two calibration methods.

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BIAS TRENDS AVERAGED OVER THE SOUTHERN HEMISPHERE We now consider only the AF FOV and overlay Tp7 in green (adjusted to zero time mean). For descending passes variations in Tp7 and the biases seem to exhibit a clear phase relationship. For ascending passes the relationship between Tp7 and the biases is less clear. Descending pass Tp7 adjusted to zero time meanAscending pass Tp7 adjusted to zero time mean

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BIAS TRENDS AVERAGED OVER THE SOUTHERN HEMISPHERE We now consider the difference between descending and ascending pass biases for both calibration methods. A clear annual cycle is apparent with similar trends in the AF and EAF fields of view. Also, between November and March the AF and EAF biases separate (circled in yellow). This separation in more pronounced in Cal L1 than in the 1-slope results. Possibly related to error in galactic scattering model Separation between EAF and AF biases greater for Cal L1 than for 1-slope model. Possibly related to differences in the sets orbits used.

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BIAS TRENDS AVERAGED OVER THE SOUTHERN HEMISPHERE We now overlay the (zero mean) difference between descending and ascending Tp7. There is some apparent correspondence between variations in Tp7 and the annual cycle in the biases:

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CONCLUSION #1 The latitudinally averaged AF and EAF bias trends for the 1-Slope and Calibrated L1 methods are very similar. Differences may be related to differences in the orbit sets used for analysis. Both methods yield a strong seasonal cycle in (Tx+Ty)/2 bias of about 1 kelvin in peak-to-peak amplitude with a distinct minimum in the reconstructed brightness temperatures toward the end of each year. This cycle is associated with a seasonal cycle in the mean retrieved sea surface salinity (SSS) bias of nearly 2 psu in peak-to- peak amplitude (without periodic OTT correction).

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A LOOK AT THE BIAS TRENDS Having established the method used to evaluate the bias between the reconstructed and model brightness temperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), we now move on to present the biases for both the most recent ESA reprocessing campaign, which employed the ‘1-slope’ loss model, and the ‘calibrated L1’ method recently proposed. Below is an outline of which follows: 1.Examination of biases averaged over longitude and latitude, including a look at coherence with variations in the corresponding average Tp7; 2.Examination of the potential impact of geophysical parameters on descending-ascending bias differences; 3.Examination of the correlation between bias variations and variations in Tp7 and several geophysical parameters; 4.Examination of time-latitude structure of the bias, which highlights the strong high-latitude bias variations late in each year.

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We now briefly examine the extent to which the scene bright model may contribute to the descending-ascending difference in (Tx+Ty)/2. This should provide an indication of the possible influence of variability in the scene sampling. The result is that only scattered galacitc radiation contributes significantly to the descending-ascending differences. IMPACT OF GEOPHYSICAL PARAMETERS ON THE BIAS TRENDS Specular emission refl galactic Rough emissionatm emission scat galactic Only the scattered/reflected galactic radiation contributes significantly to descending- ascending differences in (Tx+Ty)/2 Green curves = modeled contributions to desc-asc (Tx+Ty)/2 from various radiation sources

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CONCLUSION #2 Of all main geophysical contributions to the descending-ascending differences in (Tx+Ty)/2, scattered galactic radiation is the only significant one, and this is taken into account in the bias calculations. Some potential for error remains in this model, but the impact should be less than a few tenths of a kelvin and limited to descending passes in September-October.

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A LOOK AT THE BIAS TRENDS Having established the method used to evaluate the bias between the reconstructed and model brightness temperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), we now move on to present the biases for both the most recent ESA reprocessing campaign, which employed the ‘1-slope’ loss model, and the ‘calibrated L1’ method recently proposed. Below is an outline of which follows: 1.Examination of biases averaged over longitude and latitude, including a look at coherence with variations in the corresponding average Tp7; 2.Examination of the potential impact of geophysical parameters on descending-ascending bias differences; 3.Examination of the correlation between bias variations and variations in Tp7 and several geophysical parameters; 4.Examination of time-latitude structure of the bias, which highlights the strong high-latitude bias variations late in each year.

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CROSS CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL PARAMETERS, AND TP7 In the slides that follow we present the cross correlations between a number of variables averaged over the alias- free field of view and expressed as functions of latitude and time. The correlations are computed over variations in both time and latitude.

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CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL PARAMETERS, AND TP7 We begin this section by noting that there is a very large cross correlation between Tp7 and the bias in (Tx+Ty)/ in descending passes. The correlation exceeds 0.9 in magnitude between 60 o S and 5 o N latitude!

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CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL PARAMETERS, AND TP7 We have computed the correlation coefficient between (Tx+Ty)/2 and various AF-FOV averaged parameters, including Tp7 (lower right panel). SLP Tp7WSCWV SSTSSS

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CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL PARAMETERS, AND TP7 For descending passes the large correlation between the bias in (Tx+Ty)/2 and the parameters shown involves Tp7! SLP Tp7WSCWV SSTSSS

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CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL PARAMETERS, AND TP7 For ascending passes the situation is less clear: SLP Tp7WSCWV SSTSSS

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We next arrange the cross correlations between all combinations of variables into a matrix. Note the strong correlation between wind speed and (Tx+Ty)/2 (st1) that appears to be related to the correlation between wind speed and Tp7 (owing to latitude dependence of these two variables): CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL PARAMETERS, AND TP7 DESCENDING PASSES St1=(Tx+Ty)/2 Correlations between wind speed, tp7 and first stokes! Correlations between 1)sst and sss; 2)sst and columnar water vapor; 3)sss and slp.

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ASCENDING PASSES St1=(Tx+Ty)/2 CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, GEOPHYSICAL PARAMETERS, AND TP7 The correlation matrix for ascending passes does not exhibit the same dominant correlation between Tp7 and the first Stokes parameter. Much smaller correlations between wind speed, tp7 and first stokes for ascending passes than for descending passes!

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CORRELATIONS BETWEEN VARIATIONS IN (Tx+Ty)/2, FORWARD MODEL COMPONENTS, AND TP7 We next formed similar matrices for various components of the scene brightness model, including roughness emission (rgh), atmospheric emission (atm), specular emission (flt), and galactic reflection (gal): DESCENDING PASSES Correlations between roughness emission, tp7 and first stokes!

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A LOOK AT THE BIAS TRENDS Having established the method used to evaluate the bias between the reconstructed and model brightness temperatures in the instrument polarization basis (Tx,Ty,Uxy,Vxy), we now move on to present the biases for both the most recent ESA reprocessing campaign, which employed the ‘1-slope’ loss model, and the ‘calibrated L1’ method recently proposed. Below is an outline of which follows: 1.Examination of biases averaged over longitude and latitude, including a look at coherence with variations in the corresponding average Tp7; 2.Examination of the potential impact of geophysical parameters on descending-ascending bias differences; 3.Examination of the correlation between bias variations and variations in Tp7 and several geophysical parameters; 4.Examination of time-latitude structure of the bias, which highlights the strong high-latitude bias variations late in each year.

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DESCENDING PASSES, REPROCESSING DATA The bias trends presented earlier involved averages over latitude from 60 o S to 5 o N. But there is a seasonal evolution of the latitudinal (orbital time scale) variation of bias, especially in descending passes.

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DESCENDING PASSES, CAL L1 TEST DATA The same plot but for the calibrated L1 data shows trends similar to those for the reprocessing data except for a slightly higher amplitude in the seasonal oscillation. High latitude positive bias in (Tx+Ty)/2 just after the sun eclipse

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DESCENDING PASSES, REPROCESSING DATA The seasonal evolution of the latitudinal (orbital time scale) variation of bias is smaller in amplitude in ascending than in descending passes, but there is a strong seasonal cycle in the latitudinally averaged bias:

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DESCENDING PASSES, TP7 The bias north of 30 o N late in the year corresponds to a negative deviation in Tp7: High latitude negative deviation in Tp7 in the same area.

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DESCENDING PASSES, TP6 Tp6 also exhibits a (much smaller) negative deviation in the same area: High latitude negaitve deviation in Tp6 in the same area.

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DESCENDING PASSES, RMS ERROR The spatial AF-FOV RMS error between model and the data exhibits a clear increase from 2010 to 2011, but only toward the end of the year. RMS error increases significantly from end of 2010 to end of 2011.

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DESCENDING PASSES, SUN ALIAS BRIGHTNESS The sun angle from boresight exhibits a pattern quite coherent with the evolution of the spatial RMS error. In particular the RMS error is large where the sun angle from boresight is small: Sun angle from boresight is at a minimum in this high- latitude region at the end of the year.

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DESCENDING PASSES, SUN ALIAS BRIGHTNESS The portion of the time-latitude plots where the sun is eclipsed is very small but is near the strong RMS error and bias features: Sun is eclipsed by the earth over a very small portion of the hovmoller plots.

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DESCENDING PASSES, SUN ALIAS BRIGHTNESS Coincidentally, the average bias in a disc of radius 0.1 in dc coordinates centered on the lower left direct sun alias exhibits maximum in the same high-latitude area towards the end of 2010 and 2011: Lower-left sun alias bias in (Tx+Ty)/2 also slightly increases from 2010 to 2011.

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EVOLUTION OF SUN BRIGHTNESS TEMPERATURE AT L-BAND For reference, the sun brightness temperature at L-band increased significantly between the end of 2010 and the end of 2011: Time period of high latitude biases Big jump in sun L-band Tb from end of 2010 to end of 2011!

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CONCLUSION #4 Time-latitude plots of the AF-FOV mean bias between reconstructed and modeled (Tx+Ty)/2 reveal significant latitudinal structure that is not revealed in the latitudinally averaged bias curves. This structure is especially strong in descending passes north of about 30 o N toward the end of each year. Moreover, this region of high latitudinaly gradient in the bias coincides with a region of high spatial RMS error, a minimum in the sun angle from boresight, strongly varying Tp7 and Tp6, and strongly varying (Tx+Ty)/2 bias averaged within a disc of radius 0.1 dc units centered on the lower-left sun alias. The spatial RMS error in this high-latitude region is much stronger in 2011 than in Coincidentally, the sun brightness temperature at L-band increases significantly between the end of 2010 and the end of 2011.

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SUMMARY OF CONCLUSIONS 1.Both the ‘1-Slope’ and ‘Calibrated L1’ calibration methods yield a strong seasonal cycle in (Tx+Ty)/2 bias of about 1 kelvin in peak-to-peak amplitude with a distinct minimum in the reconstructed brightness temperatures toward the end of each year. This cycle is associated with a seasonal cycle in the mean retrieved sea surface salinity (SSS) bias of nearly 2 psu in peak-to-peak amplitude (without periodic OTT correction). 2.Of all main geophysical contributions to the descending-ascending differences in (Tx+Ty)/2, scattered galactic radiation is the only significant one, and this is taken into account in the bias calculations. 3.Descending passes exhibit strong correlation between (Tx+Ty)/2 bias and Tp7 (correlation coefficient around -0.9). 4.Time-latitude plots of the AF-FOV mean bias between reconstructed and modeled (Tx+Ty)/2 reveal significant latitudinal structure that is not revealed in the latitudinally averaged bias curves. This structure is especially strong in descending passes north of about 30 o N toward the end of each year. A number of other parameters also exhibit patterns coherent with the pattern of bias.